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RichaChampion
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RichaChampion
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crunchboss
Thanks sir, This is so informative you can convert this into a blog on magoosh. I have one more question sir as you said "Here, there are thousands of ways to meet condition Y without meeting condition X---one could be in New York City or Chicago or Washington, DC or Santa Fe, New Mexico, to name just a few examples. "

Even though there are thousands of ways to meet the condition why, but then what is the connection between X and Y if X is not essential for Y to exist? Did you get my point sir?

If I am in Berkeley, California, then I am in the United States of America.
X = I am in Berkeley, California
Y = I am in the United States of America

The above If Then construction i correct or not?
Dear crunchboss,
I'm happy to respond. :-)

First, I'll say the example If-Then statement you gave is grammatically and logically correct. In fact, we can drop the word "then."
If I am in Berkeley, California, I am in the United States of America.

My friend, I want to point out that we are discussing here issues of formal logic, which are wonderful in their own right, but these really are beyond anything you need to know for the GMAT. I will begin with something from mathematics, which might be a little clearer. It's important to appreciate the profound logical asymmetry of the if-then structure.

If a shape is a square, then the shape is a rectangle. = true
This is logically equivalent to the following statement:
Every square is a rectangle. = true

The logical connection between is that if something is a square, it must be a rectangle: there's no way to be a square without also being a rectangle. BUT, and this is important, there are a continuous infinity of possible rectangles that are not squares. The number of rectangles that are not squares infinitely outnumbers the ones that are squares, and yet every square is a rectangle.

In general, if we are given the statement If X, then Y, and if we know that statement is true, then we know that condition X always leads to condition Y and that it is impossible to have condition X without having Y also. At the same time, it leaves open the possibility that there are many other possibilities for condition Y, many other ways for condition Y to exist, without condition X being involved.

With the Berkeley example: if I am in Berkeley, I have to be in the USA; there is absolutely no way I could be in Berkeley and not be in the USA. It would logically equivalent to the statement, "Everyone in Berkeley is in the USA." At the same time, there are 1000s of ways to be in the USA without being in Berkeley.

Does all this make sense?
Mike :-)
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RichaChampion
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mikemcgarry
crunchboss
Thanks sir, This is so informative you can convert this into a blog on magoosh. I have one more question sir as you said "Here, there are thousands of ways to meet condition Y without meeting condition X---one could be in New York City or Chicago or Washington, DC or Santa Fe, New Mexico, to name just a few examples. "

Even though there are thousands of ways to meet the condition why, but then what is the connection between X and Y if X is not essential for Y to exist? Did you get my point sir?

If I am in Berkeley, California, then I am in the United States of America.
X = I am in Berkeley, California
Y = I am in the United States of America

The above If Then construction i correct or not?
Dear crunchboss,
I'm happy to respond. :-)

First, I'll say the example If-Then statement you gave is grammatically and logically correct. In fact, we can drop the word "then."
If I am in Berkeley, California, I am in the United States of America.

My friend, I want to point out that we are discussing here issues of formal logic, which are wonderful in their own right, but these really are beyond anything you need to know for the GMAT. I will begin with something from mathematics, which might be a little clearer. It's important to appreciate the profound logical asymmetry of the if-then structure.

If a shape is a square, then the shape is a rectangle. = true
This is logically equivalent to the following statement:
Every square is a rectangle. = true

The logical connection between is that if something is a square, it must be a rectangle: there's no way to be a square without also being a rectangle. BUT, and this is important, there are a continuous infinity of possible rectangles that are not squares. The number of rectangles that are not squares infinitely outnumbers the ones that are squares, and yet every square is a rectangle.

In general, if we are given the statement If X, then Y, and if we know that statement is true, then we know that condition X always leads to condition Y and that it is impossible to have condition X without having Y also. At the same time, it leaves open the possibility that there are many other possibilities for condition Y, many other ways for condition Y to exist, without condition X being involved.

With the Berkeley example: if I am in Berkeley, I have to be in the USA; there is absolutely no way I could be in Berkeley and not be in the USA. It would logically equivalent to the statement, "Everyone in Berkeley is in the USA." At the same time, there are 1000s of ways to be in the USA without being in Berkeley.

Does all this make sense?
Mike :-)

Mike Mc Garry Sir - Fantatstic! :-D